Linearized unsteady viscous turbomachinery flows using hybrid grids

The paper describes the theory and the numerical implementation of a three- dimensional finite volume scheme for the solution of the linearized, unstea dy Favre-averaged Navier-Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangle s and quadrilaterals in tw dimensions, and of tetrahedra, triangular prisms , and hexahedra in three dimensions. The linearized unsteady viscous flow e quations are derived by assuming small harmonic perturbations from a steady -state flow and the resulting equations art, solved using 11 pseudo-time ma rching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow comp utations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element mes hes, the use of a Laplacian operator, which results in a nearest neighbor s tencil, and the full linearization of the Spalart-Allmaras turbulence model . Four different test cases are presented for the validation of the propose d method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the secon d test case is to check the computational results against the asymptotic an alytical solution derived by Lighthill for an unsteady laminar flow. The th ird test case examines the implications of using inviscid, frozen-turbulenc e, and fully turbulent models when linearizing the unsteady flow over a tra nsonic turbine blade, the so-called 11th International Standard Configurati on. The final test case is a rotor/stator interaction, which not only check s the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady , flow data for the last two cases and good overall agreement was obtained.